Rogue waves, also called freak waves, giant waves or killer waves have attracted considerable attentions. A rogue wave is a large-amplitude local wave, short-lived wave, meet in an ocean that appears from nowhere and disappears without a trace. Rogue waves appear not only in oceanic conditions [1]}, but also in optics [2]}, superfluids [3]}, Bose-Einstein condensates [4]} and in the form of capillary waves [5]}. In any of these disciplines, new studies of rogue waves enrich the concept and lead to progress toward a comprehensive understanding of this still mysterious phenomenon.
The first-order rational solution for the nonlinear Schr\(\ddot{o}\) dinger equation (NLSE) was given by Peregrine [6]}. Akhmediev and co-workers have calculated the simplest rogue wave solutions for the NLSE [7]}, [8]}. The construction of higher-order analogues is actually a challenging problem. The construction of higher-order rogue wave solutions needs a simple approach which is the generalized Dardoux transformation (DT). This approach was proposed by Guo et al [9]}.
